Embodiments herein generally relate to rollers used to support and drive closed loop belts within devices such as printing devices and more particularly to inertia compensated roller design.
U.S. Pat. No. 3,659,767 to J. R. Martin (hereinafter referred to as “Martin” and fully incorporated herein by reference) discloses a “dancer” roll used in web transportation. The dancer roll is a roller over which the web passes as it is being transported from a roll (medium source) to another roll. The dancer roll attenuates and insulates motion disturbances form reaching the motion crucial areas of the web. The dancer roll was originally meant to be used in the open loop belt/web transportation (the open loop belt/web system may be simply referred to as a web), but its area of application may be expanded to include closed loop belts. A closed loop belt may be simply referred to as a belt.
More specifically, Martin describes that a recurring problem in systems for performing operations on belt/webs of paper, cloth or other suitable material is the regulation of belt/web tension. Such problems may arise in a number of arts such as printing, film and plastic processing, and magnetic tape recording. In the operation of high speed continuous printing presses the problems of regulating belt/web tension are particularly important. Failure to prevent tension changes in a moving belt/web results in stretching and shrinking of the belt/web along its length. When this occurs in the region in which the belt/web is being imaged, it leads to defects in the printed product such as slurring, doubling and ghosting of images, color mis-registration, and if the tension becomes too great, breaking of the belt/web and interruption of operations.
There are several causes of tension fluctuation in belts/webs. These include variations in the belt/web's modulus of elasticity due to material irregularities or changes in temperature or humidity, rolls which have flat spots or are elliptical in cross section, drifting in the speed of the various drive rolls and the supply roll, irregularities in the operation of braking mechanisms, and the operation of flying pasters which join one supply roll to another while the press is in operation.
A number of means have been developed to regulate or control tension, none of which completely solve the problem of preventing transient changes or fluctuations in tension in one region of the belt/web from causing tension changes in other regions. One approach has been to utilize one or more dancer rolls—floating rotating cylinders each of which, when placed between two rolls and offset therefrom, constrains the belt/web into a loop and exerts force on the bight of the loop. This force, which may be a result of the weight of the dancer or of a force exerted on the dancer by a spring, a fluid pressure actuated cylinder, or an external weight, or some combination thereof, establishes an average level of tension in the loop. It does not, however, completely compensate for changes in belt/web tension on one side of the dancer which usually cause tension changes on the other side of the dancer.
Martin explains that devices have been developed in which the position of a roller, which changes as the belt/web tension changes, is sensed to produce an input signal for a control circuit. The control circuit may be used to adjust another parameter which can affect belt/web tension such as the speed of the supply roll or of drive rolls thus readjusting the belt/web tension to compensate for the initial change and restoring the dancer to its initial position.
In order to address the foregoing issues, embodiments herein comprise an apparatus such as a photoreceptor belt or other belt system in a printing apparatus (e.g., an electrostatographic and a xerographic machine, etc.); an associated method of making a floating roller; and an associated computer program. The apparatus includes a tensioning system having a plurality of rollers. At least one of the rollers (e.g., a drive roller) is adapted to contact, support, and move a closed loop belt, and other rollers (e.g., support rollers or idle rollers) are adapted to freely rotate so as to contact and support the closed loop belt.
A floating roller also freely rotates so as to contact and support the closed loop belt. The floating roller is mounted to rotate and travel along at least one linear path or pivot around some center to move the floating roller center. The drive roller and support rollers are in fixed positions while the floating roller moves relative to the other rollers to maintain the constant tension in the closed loop belt.
The relationship between mass of the floating roller and rotational inertia of the floating roller controls the tensioning system to maintain a constant tension on the closed loop belt. More specifically, the relationship between mass of the floating roller and rotational inertia of the floating is based on the following equation:
  M  ≈            (              1        -                              T            _                    Ebw                    )        ⁢                  sin        2            ⁡              (                  α          /          2                )              ⁢          J              R        2            where M is the mass of the floating roller, J is the rotational inertia of the floating roller, R is the external radius of the floating roller, E is a Young's modulus of the closed loop belt, b is the thickness of the closed loop belt, w is the width of the closed loop belt, T is the tension force on the closed loop belt and α is an angle (wrap angle) over which the closed loop belt contacts the floating roller.
Similarly, a method embodiment of designing a floating roller in a tensioning system adapted to support a closed loop belt comprises inputting an external radius of the floating roller, a measure of elasticity of the material, a thickness of the material, a width of the material, and angles at which the material contacts the floating roller; and adjusting a mass of the floating roller and a rotational inertia of the floating roller such that the floating roller maintains a constant tension on the closed loop belt as the material is passing through the tensioning system based on the following equation:
  M  ≈            (              1        -                              T            _                    Ebw                    )        ⁢                  sin        2            ⁡              (                  α          /          2                )              ⁢          J              R        2            where M is the mass of the floating roller, J is the rotational inertia of the floating roller, R is the external radius of the floating roller, E is a Young's modulus of the closed loop belt, b is the thickness of the closed loop belt, w is the width of the closed loop belt, T is the tension force on the closed loop belt and α is an angle (wrap angle) at which the closed loop belt contacts the floating roller.
These and other features are described in, or are apparent from, the following detailed description.